Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	51×	body	640	valid
10.0ms	225×	body	80	nan
9.0ms	36×	body	1280	valid
7.0ms	133×	body	80	valid
4.0ms	26×	body	320	valid
1.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	11
0	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `hypot-def` `flip--`

Counts

4 → 758

Calls

4 calls:

12.0ms	(sqrt (+ x 1.0))
13.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
109.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series372.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (+ x 1.0))
108.0ms	(/ 1.0 (sqrt (+ x 1.0)))
50.0ms	(/ 1.0 (sqrt x))
175.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts

770 → 770

Iterations

Iter	Nodes
done	5000
2	3579
1	1587
0	702

prune4.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 18.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.4b	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`pow1`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `times-frac` `pow1/2` `pow-prod-down` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `distribute-lft-out` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `fma-neg` `sqrt-unprod` `diff-log` `div-sub` `prod-diff` `-commutative` `hypot-def` `div-inv`

Counts

4 → 98

Calls

4 calls:

9.0ms	(sqrt (+ x 1.0))
47.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
13.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series623.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt (+ x 1.0))
340.0ms	(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
75.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
159.0ms	(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify1.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5005
2	2181
1	591
0	206

prune702.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 18.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
2.7b	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

86×	`pow1`
37×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
17×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `associate-*r/`
14×	`sqrt-div`
11×	`sqrt-prod`
10×	`*-un-lft-identity`
9×	`associate-r`
8×	`associate-l` `pow-sqr` `pow-prod-up` `add-cube-cbrt`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`expm1-log1p-u` `frac-times` `pow-plus` `log1p-expm1-u` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-*l/`
1×	`sub-neg` `flip3--` `fma-neg` `sqrt-unprod` `diff-log` `prod-diff` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

28.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
93.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
39.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
71.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
44.0ms	(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
32.0ms	(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
26.0ms	(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify1.5s

Counts

144 → 144

Iterations

Iter	Nodes
done	5003
2	1524
1	491
0	183

prune507.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.1b	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
18×	`associate-*r/`
14×	`flip3-+` `sqrt-div` `flip-+`
13×	`pow1` `*-un-lft-identity`
11×	`add-cube-cbrt` `sqrt-prod`
10×	`associate-r`
8×	`frac-times` `associate-/r/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `unswap-sqr`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`sqrt-pow1` `pow1/2` `*-commutative`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `associate-/r*` `sum-log` `fma-def` `frac-2neg` `distribute-lft-in` `sqrt-unprod` `div-inv` `distribute-lft-out`

Counts

4 → 112

Calls

4 calls:

12.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
66.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
20.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
53.0ms	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

series999.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
280.0ms	(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
61.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
558.0ms	(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

simplify2.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5002
2	3341
1	849
0	272

prune464.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes95.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

580.0ms	7962×	body	80	nan
354.0ms	1862×	body	640	valid
249.0ms	1143×	body	1280	valid
166.0ms	4043×	body	80	valid
91.0ms	630×	body	320	valid
21.0ms	322×	body	160	valid